Finite Group Databasebeta

← C151×#18366 #50323291

Subgroups — C151×#18366 #50323291

Order 38656.

1048 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3493×C151C211yesmaximal, characteristic, complemented
2#3217×C151C212yesmaximal, complemented
3#2619×C151C211yesmaximal, characteristic, complemented
4#1600×C151C214yesmaximal, complemented
5#1599×C151C212yesmaximal, complemented
6#1598×C151C212yesmaximal, complemented
7#1512×C151C212yesmaximal, complemented
8#1464×C151C211yesmaximal, characteristic, complemented
9#556×C151—22no—
10#555×C151—22no—
11#553×C151—22no—
12#552×C151—22no—
13#544×C151C2211yescharacteristic
14#538×C151—21no—
15#538×C151C2212yes—
16#537×C151C2211yescharacteristic
17C2×#127×C151C2211yescharacteristic
18#529×C151—21no—
19#529×C151C2212yes—
20#525×C151—21no—
21C2×#121×C151—21no—
22#520×C151—21no—
23C2×#117×C151C2211yescharacteristic
24#496×C151—22no—
25#490×C151—22no—
26#460×C151—22no—
27#459×C151—22no—
28#450×C151C2214yes—
29#447×C151C2214yes—
30#432×C151C2212yes—
31#394×C151—21no—
32#394×C151C2212yes—
33#392×C151—21no—
34#392×C151C2212yes—
35#390×C151—21no—
36#382×C151C2211yescharacteristic
37#328×C151C2214yes—
38#327×C151C2214yes—
39#324×C151C2212yes—
40#323×C151C2212yes—
41C2×#41×C151—21no—
42C22×D4×C151—21no—
43C22×D4×C151—21no—
44C22×D4×C151—22no—
45C22×D4×C151C2312yes—
46C23×C4×C151D411yescharacteristic
47C2×SD16×C151—24no—
48C2×D8×C151—24no—
49C4⋊Q8×C151—22no—
50#127×C151—22no—
51#127×C151—22no—
52#126×C151—22no—
53#126×C151—22no—
54#126×C151—22no—
55#126×C151—22no—
56#125×C151—21no—
57#125×C151—22no—
58#125×C151D412yescomplemented
59#124×C151—21no—
60#124×C151—22no—
61#124×C151—22no—
62#124×C151D412yescomplemented
63#123×C151—22no—
64#123×C151—22no—
65#123×C151—22no—
66C22⋊Q8×C151—21no—
67C22⋊Q8×C151—21no—
68C22⋊Q8×C151—21no—
69C22⋊Q8×C151—22no—
70C22⋊Q8×C151C2312yes—
71#121×C151—21no—
72#121×C151—21no—
73#121×C151—22no—
74#121×C151—22no—
75#121×C151—22no—
76#121×C151—21no—
77#121×C151—44no—
78#121×C151C2312yes—
79#120×C151—22no—
80C4×Q8×C151—22no—
81C4×Q8×C151—21no—
82C4×Q8×C151D412yescomplemented
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151—21no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151D412yescomplemented
90#117×C151—22no—
91#117×C151—22no—
92#117×C151—21no—
93#117×C151—22no—
94#117×C151—22no—
95#117×C151—22no—
96C2×C4⋊C4×C151—22no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151D411yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C22⋊C4×C151—22no—
101C2×C22⋊C4×C151—22no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151D411yescharacteristic
104C2×C22⋊C4×C151C2311yescharacteristic
105C2×C42×C151D411yescharacteristic
106C2×C42×C151C2311yescharacteristic
107C4⋊C8×C151—22no—
108#102×C151—24no—
109#102×C151—24no—
110C22⋊C8×C151C2314yes—
111#97×C151—22no—
112#95×C151—21no—
113#95×C151C2312yes—
114C24×C151—22no—
115C24×C151C2×D411yescharacteristic
116#41×C151—42no—
117#41×C151—42no—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×Q8×C151C2×D412yes—
121C2×D4×C151—21no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—21no—
126C2×D4×C151—24no—
127C2×D4×C151—42no—
128C2×D4×C151—42no—
129C2×D4×C151—44no—
130C2×D4×C151—41no—
131C2×D4×C151—41no—
132C2×D4×C151—42no—
133C2×D4×C151—82no—
134C2×D4×C151—82no—
135C2×D4×C151—82no—
136C2×D4×C151—82no—
137C2×D4×C151C2×D412yes—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—41no—
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2411yescharacteristic
152SD16×C151—84no—
153D8×C151—84no—
154C2×C8×C151—24no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—42no—
168C4⋊C4×C151C2×D412yes—
169C4⋊C4×C151C2×D412yes—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—22no—
175C22⋊C4×C151—22no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—22no—
181C22⋊C4×C151—44no—
182C22⋊C4×C151—82no—
183C22⋊C4×C151—82no—
184C42×C151—22no—
185C42×C151—22no—
186C42×C151—21no—
187C42×C151—21no—
188C42×C151—22no—
189C42×C151C2×D412yes—
190C42×C151C2×D412yes—
191C23×C151—21no—
192C23×C151—22no—
193C23×C151—21no—
194C23×C151—21no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151C22×D411yescharacteristic
205Q8×C151—42no—
206Q8×C151—42no—
207Q8×C151—81no—
208D4×C151—42no—
209D4×C151—42no—
210D4×C151—44no—
211D4×C151—44no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—82no—
215D4×C151—82no—
216D4×C151—84no—
217D4×C151—82no—
218D4×C151—81no—
219D4×C151—82no—
220D4×C151—88no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—22no—
226C2×C4×C151—21no—
227C2×C4×C151—22no—
228C2×C4×C151—21no—
229C2×C4×C151—22no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—44no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—82no—
241C2×C4×C151—82no—
242C2×C4×C151#12011yescharacteristic
243C2×C4×C151#12011yescharacteristic
244C2×C4×C151#12012yes—
245C2×C4×C151AGL(1,ℤ/8)12yes—
246C2×C4×C151C22×D412yes—
247C8×C151—44no—
248C22×C151—21no—
249C22×C151—21no—
250C22×C151—42no—
251C22×C151—41no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—41no—
255C22×C151—42no—
256C22×C151—41no—
257C22×C151—81no—
258C22×C151—82no—
259C22×C151—82no—
260C22×C151—82no—
261C22×C151—82no—
262C22×C151—82no—
263C22×C151—82no—
264C22×C151—82no—
265C22×C151C2×#12011yescharacteristic
266C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C151#57511yescharacteristic
268C4×C151—22no—
269C4×C151—21no—
270C4×C151—21no—
271C4×C151—22no—
272C4×C151—22no—
273C4×C151—42no—
274C4×C151—41no—
275C4×C151—42no—
276C4×C151—41no—
277C4×C151—42no—
278C4×C151—82no—
279C2×C151—21no—
280C2×C151—21no—
281C2×C151—82no—
282C2×C151—81no—
283C2×C151—162no—
284C2×C151#300611yescharacteristic
285C2×C151#302111yescharacteristic
286C2×C151#302711yescharacteristic
287#18366C15111yesmaximal, characteristic, direct product factor, Sylow
288C151#1836611yescharacteristic, direct product factor, Sylow
289#3493C2×C15111yescharacteristic, complemented
290#3217C2×C15112yescomplemented
291#2619C2×C15111yescharacteristic, complemented
292#1600C2×C15114yescomplemented
293#1599C2×C15112yescomplemented
294#1598C2×C15112yescomplemented
295#1512C2×C15112yescomplemented
296#1464C2×C15111yescharacteristic, complemented
297#556—22no—
298#555—22no—
299#553—22no—
300#552—22no—
301#544C22×C15111yescharacteristic
302#538—21no—
303#538C22×C15112yes—
304#537C22×C15111yescharacteristic
305C2×#127C22×C15111yescharacteristic
306#529—21no—
307#529C22×C15112yes—
308#525—21no—
309C2×#121—21no—
310#520—21no—
311C2×#117C22×C15111yescharacteristic
312#496—22no—
313#490—22no—
314#460—22no—
315#459—22no—
316#450C22×C15114yes—
317#447C22×C15114yes—
318#432C22×C15112yes—
319#394—21no—
320#394C22×C15112yes—
321#392—21no—
322#392C22×C15112yes—
323#390—21no—
324#382C22×C15111yescharacteristic
325#328C22×C15114yes—
326#327C22×C15114yes—
327#324C22×C15112yes—
328#323C22×C15112yes—
329C2×#41—21no—
330C22×D4—22no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4C23×C15112yes—
334C23×C4D4×C15111yescharacteristic
335C2×SD16—24no—
336C2×D8—24no—
337C4⋊Q8—22no—
338#127—22no—
339#127—22no—
340#126—22no—
341#126—22no—
342#126—22no—
343#126—22no—
344#125—21no—
345#125—22no—
346#125D4×C15112yescomplemented
347#124—21no—
348#124—22no—
349#124—22no—
350#124D4×C15112yescomplemented
351#123—22no—
352#123—22no—
353#123—22no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—22no—
358C22⋊Q8C23×C15112yes—
359#121—21no—
360#121—21no—
361#121—22no—
362#121—22no—
363#121—22no—
364#121—21no—
365#121—44no—
366#121C23×C15112yes—
367#120—22no—
368C4×Q8—22no—
369C4×Q8—21no—
370C4×Q8D4×C15112yescomplemented
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4D4×C15112yescomplemented
378#117—22no—
379#117—22no—
380#117—21no—
381#117—22no—
382#117—22no—
383#117—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C15111yescharacteristic
387C2×C4⋊C4C23×C15111yescharacteristic
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4D4×C15111yescharacteristic
392C2×C22⋊C4C23×C15111yescharacteristic
393C2×C42D4×C15111yescharacteristic
394C2×C42C23×C15111yescharacteristic
395C4⋊C8—22no—
396#102—24no—
397#102—24no—
398C22⋊C8C23×C15114yes—
399#97—22no—
400#95—21no—
401#95C23×C15112yes—
402C24—22no—
403C24C2×D4×C15111yescharacteristic
404#41—42no—
405#41—42no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×D4×C15112yes—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—24no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—42no—
421C2×D4—82no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4C2×D4×C15112yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C24×C15111yescharacteristic
440SD16—84no—
441D8—84no—
442C2×C8—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4C2×D4×C15112yes—
457C4⋊C4C2×D4×C15112yes—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—44no—
470C22⋊C4—82no—
471C22⋊C4—82no—
472C42—22no—
473C42—22no—
474C42—21no—
475C42—21no—
476C42—22no—
477C42C2×D4×C15112yes—
478C42C2×D4×C15112yes—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—21no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C22×D4×C15111yescharacteristic
493Q8—42no—
494Q8—42no—
495Q8—81no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—44no—
500D4—42no—
501D4—42no—
502D4—82no—
503D4—82no—
504D4—84no—
505D4—82no—
506D4—81no—
507D4—82no—
508D4—88no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4#120×C15111yescharacteristic
531C2×C4#120×C15111yescharacteristic
532C2×C4#120×C15112yes—
533C2×C4AGL(1,ℤ/8)×C15112yes—
534C2×C4C22×D4×C15112yes—
535C8—44no—
536C22—21no—
537C22—21no—
538C22—42no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—41no—
545C22—81no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22C2×#120×C15111yescharacteristic
554C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
555C22#575×C15111yescharacteristic
556C4—22no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—22no—
561C4—42no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—82no—
567C2—21no—
568C2—21no—
569C2—81no—
570C2—82no—
571C2—162no—
572C2#3006×C15111yescharacteristic
573C2#3021×C15111yescharacteristic
574C2#3027×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3493×C151C2semidirect
2. #3217×C151C2semidirect
3. #2619×C151C2semidirect
4. #1600×C151C2semidirect
5. #1599×C151C2semidirect
6. #1598×C151C2semidirect
7. #1512×C151C2semidirect
8. #1464×C151C2semidirect
58. #125×C151D4semidirect
62. #124×C151D4semidirect
82. C4×Q8×C151D4semidirect
89. C4×D4×C151D4semidirect
287. #18366C151direct (N × H)
288. C151#18366direct (N × H)
289. #3493C2×C151semidirect
290. #3217C2×C151semidirect
291. #2619C2×C151semidirect
292. #1600C2×C151semidirect
293. #1599C2×C151semidirect
294. #1598C2×C151semidirect
295. #1512C2×C151semidirect
296. #1464C2×C151semidirect
346. #125D4×C151semidirect
350. #124D4×C151semidirect
370. C4×Q8D4×C151semidirect
377. C4×D4D4×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3493×C1512
#3217×C1512
#2619×C1512
#1600×C1512
#1599×C1512
#1598×C1512
#1512×C1512
#1464×C1512
#18366151